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<title>CSE 4/562 - Spring 2018</title>
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CSE 4/562 - Database Systems
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<div class="slides">
<section>
<h1>Cost Based Optimization</h1>
<h3>CSE 4/562 – Database Systems</h3>
date
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<h5>February 28, 2018</h5>
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</section>
<!-- ============================================ -->
<section>
<section>
<h3>General Query Optimizers</h3>
<ol style="font-size: 60%">
<li>Apply blind heuristics (e.g., push down selections)</li>
<li>Enumerate all possible <i>execution plans</i> by varying (or for a reasonable subset)
<ul>
<li>Join/Union Evaluation Order (commutativity, associativity, distributivity)</li>
<li>Algorithms for Joins, Aggregates, Sort, Distinct, and others</li>
<li>Data Access Paths</li>
</ul>
</li>
<li class="fragment highlight-blue">Estimate the cost of each execution plan</li>
<li>Pick the execution plan with the lowest cost</li>
</ol>
</section>
</section>
<section>
<section>
<p><b>Idea 1: </b> Run each plan</p>
</section>
<section>
<img src="graphics/Clipart/facepalm.jpg" class="stretch" />
<attribution>&copy; Paramount Pictures</attribution>
</section>
<section>
<p>If we can't get the exact cost of a plan, what can we do?</p>
</section>
<section>
<p class="fragment highlight-grey"><b>Idea 2: </b> Run each plan on a small sample of the data.</p>
<p style="margin-top: 50px;"><b>Idea 3: </b> Analytically estimate the cost of a plan.</p>
</section>
<section>
<h3>Plan Cost</h3>
<dl>
<div class="fragment" data-fragment-index="1"><div class="fragment highlight-grey" data-fragment-index="4">
<dt>CPU Time</dt>
<dd>How much time is spent processing.</dd>
</div></div>
<div class="fragment" data-fragment-index="2">
<dt># of IOs</dt>
<dd>How many random reads + writes go to disk.</dd>
</div>
<div class="fragment" data-fragment-index="3">
<dt>Memory Required</dt>
<dd>How much memory do you need.</dd>
</div>
</dl>
</section>
<section>
<img src="graphics/Clipart/estimation.png">
<attribution>Randal Munroe (<a href="https://creativecommons.org/licenses/by-nc/2.5/">cc-by-nc</a>)</attribution>
</section>
<section>
<h3>Remember the Real Goals</h3>
<ol>
<li class="fragment">Accurately <b>rank</b> the plans.</li>
<li class="fragment">Don't spend more time optimizing than you get back.</li>
<li class="fragment">Don't pick a plan that uses more memory than you have.</li>
</ol>
</section>
</section>
<!-- ============================================ -->
<section>
<section>
<h3>Accounting</h3>
<p class="fragment" style="margin-top: 50px;">Figure out the cost of each <b>individual</b> operator.</p>
<p class="fragment" style="margin-top: 50px;">Only count the number of IOs <b>added</b> by each operator.</p>
</section>
<section>
<table style="font-size: 70%">
<tr><th>Operation</th><th>RA</th><th>IOs Added (#pages)</th><th>Memory (#tuples)</th></tr>
<tr class="fragment" data-fragment-index="0">
<td>Table Scan</td>
<td>$R$</td>
<td class="fragment" data-fragment-index="1">$\frac{|R|}{\mathcal P}$</td>
<td class="fragment" data-fragment-index="2">$O(1)$</td>
</tr>
<tr class="fragment" data-fragment-index="3">
<td>Projection</td>
<td>$\pi(R)$</td>
<td class="fragment" data-fragment-index="4">$0$</td>
<td class="fragment" data-fragment-index="4">$O(1)$</td>
</tr>
<tr class="fragment" data-fragment-index="5">
<td>Selection</td>
<td>$\sigma(R)$</td>
<td>$0$</td>
<td>$O(1)$</td>
</tr>
<tr class="fragment" data-fragment-index="6">
<td>Union</td>
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<td>$R \uplus S$</td>
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<td>$0$</td>
<td>$O(1)$</td>
</tr>
<tr class="fragment" data-fragment-index="7">
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<td style="vertical-align: middle;">Sort <span class="fragment" data-fragment-index="8">(In-Mem)</span></td>
<td style="vertical-align: middle;">$\tau(R)$</td>
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<td class="fragment" data-fragment-index="8">$0$</td>
Index costs
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<td class="fragment" data-fragment-index="9">$O(|R|)$</td>
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</tr>
<tr>
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<td class="fragment" data-fragment-index="10">Sort (On-Disk)</td>
<td class="fragment" data-fragment-index="10">$\tau(R)$</td>
<td class="fragment" data-fragment-index="11">$\frac{2 \cdot \lfloor log_{\mathcal B}(|R|) \rfloor}{\mathcal P}$</td>
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<td class="fragment" data-fragment-index="10">$O(\mathcal B)$</td>
</tr>
<tr class="fragment" data-fragment-index="12">
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<td><span class="fragment" data-fragment-index="13">(B+Tree)</span> Index Scan</td>
<td>$Index(R, c)$</td>
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<td class="fragment" data-fragment-index="13">$\log_{\mathcal I}(|R|) + \frac{|\sigma_c(R)|}{\mathcal P}$</td>
<td class="fragment" data-fragment-index="14">$O(1)$</td>
</tr>
<tr>
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<td span class="fragment" data-fragment-index="15">(Hash) Index Scan</td>
<td span class="fragment" data-fragment-index="15">$Index(R, c)$</td>
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<td class="fragment" data-fragment-index="15">$1$</td>
<td class="fragment" data-fragment-index="16">$O(1)$</td>
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</tr>
</table>
<ol style="font-size: 50%; margin-top: 50px;">
<li class="fragment" data-fragment-index="1">Tuples per Page ($\mathcal P$) <span>– Normally defined per-schema</span></li>
<li class="fragment" data-fragment-index="1">Size of $R$ ($|R|$)</li>
<li class="fragment" data-fragment-index="10">Pages of Buffer ($\mathcal B$)</li>
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<li class="fragment" data-fragment-index="13">Keys per Index Page ($\mathcal I$)</li>
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</ol>
</section>
<section>
<table style="font-size: 70%">
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<tr><th width="300px">Operation</th><th>RA</th><th>IOs Added (#pages)</th><th>Memory (#tuples)</th></tr>
Slides
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<tr class="fragment" data-fragment-index="1">
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<td style="font-size: 60%">Nested Loop Join <span class="fragment" data-fragment-index="2">(Buffer $S$ in mem)</span></td>
<td>$R \times S$</td>
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<td class="fragment" data-fragment-index="2">$0$</td>
<td class="fragment" data-fragment-index="3">$O(|S|)$</td>
</tr>
<tr>
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<td class="fragment" data-fragment-index="4" style="font-size: 60%">Nested Loop Join (Buffer $S$ on disk)</td>
<td class="fragment" data-fragment-index="4">$R \times_{disk} S$</td>
<td class="fragment" data-fragment-index="5">$(1+ |R|) \cdot \frac{|S|}{\mathcal P}$</td>
Slides
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<td class="fragment" data-fragment-index="4">$O(1)$</td>
</tr>
<tr class="fragment" data-fragment-index="6">
<td>1-Pass Hash Join</td>
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<td>$R \bowtie_{1PH, c} S$</td>
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<td class="fragment" data-fragment-index="7">$0$</td>
<td class="fragment" data-fragment-index="7">$O(|S|)$</td>
</tr>
<tr class="fragment" data-fragment-index="8">
<td>2-Pass Hash Join</td>
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<td>$R \bowtie_{2PH, c} S$</td>
<td class="fragment" data-fragment-index="9">$\frac{2|R| + 2|S|}{\mathcal P}$</td>
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<td class="fragment" data-fragment-index="9">$O(1)$</td>
</tr>
<tr class="fragment" data-fragment-index="10">
<td>Sort-Merge Join </td>
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<td>$R \bowtie_{SM, c} S$</td>
<td class="fragment" data-fragment-index="11">[Sort]</td>
<td class="fragment" data-fragment-index="11">[Sort]</td>
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</tr>
<tr class="fragment" data-fragment-index="12">
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<td><span class="fragment" data-fragment-index="13">(Tree)</span> Index NLJ</td>
<td>$R \bowtie_{INL, c}$</td>
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<td class="fragment" data-fragment-index="13">$|R| \cdot (\log_{\mathcal I}(|S|) + \frac{|\sigma_c(S)|}{\mathcal P})$</td>
<td class="fragment" data-fragment-index="14">$O(1)$</td>
</tr>
<tr>
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<td class="fragment" data-fragment-index="15">(Hash) Index NLJ</td>
<td class="fragment" data-fragment-index="15">$R \bowtie_{INL, c}$</td>
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<td class="fragment" data-fragment-index="15">$|R| \cdot 1$</td>
<td class="fragment" data-fragment-index="16">$O(1)$</td>
</tr>
<tr class="fragment" data-fragment-index="17">
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<td><span class="fragment" data-fragment-index="18">(In-Mem)</span> Aggregate</td>
<td>$\gamma_A(R)$</td>
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<td class="fragment" data-fragment-index="18">$0$</td>
<td class="fragment" data-fragment-index="19">$adom(A)$</td>
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</tr>
<tr>
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<td class="fragment" data-fragment-index="20" style="font-size: 90%">(Sort/Merge) Aggregate</td>
<td class="fragment" data-fragment-index="20">$\gamma_A(R)$</td>
<td class="fragment" data-fragment-index="20">[Sort]</td>
<td class="fragment" data-fragment-index="20">[Sort]</td>
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</tr>
</table>
Index costs
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<ol style="font-size: 50%;">
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<li>Tuples per Page ($\mathcal P$) <span>– Normally defined per-schema</span></li>
<li>Size of $R$ ($|R|$)</li>
<li>Pages of Buffer ($\mathcal B$)</li>
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<li>Keys per Index Page ($\mathcal I$)</li>
<li class="fragment" data-fragment-index="19">Number of distinct values of $A$ ($adom(A)$)</li>
Slides
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</ol>
</section>
<section>
<p><b>Next Class: </b> How to estimate $|R|$</p>
</section>
</section>
</div></div>
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